The Moon formed about 4.5 billion years ago, not long after the Earth. It is gradually getting farther away from the Earth. (For an explanation of why this is happening, see the Tidal Evolution part of the Orbit of the Moon Wikipedia page.) Now, 4.5 billion years after the Moon formed, we happen to be at a level of scientific knowledge and technical ability such that we can both understand what an eclipse is, and can use it to study aspects of the Sun normally hidden.

So, yes, it's a coincidence that you and I are here during this particular eclipse, and more broadly speaking, that our society has been and is here during this period in the Moon's very long evolution. But it is not a coincidence that at some point in the evolution of the Moon's orbit, it happens to look close to the same size as the Sun when viewed from the surface of the Earth. That was inevitable.

rstevenson wrote:But it is not a coincidence that at some point in the evolution of the Moon's orbit, it happens to look close to the same size as the Sun when viewed from the surface of the Earth. That was inevitable.

Still, kind of special, as most moons are much smaller compared to their parent-planet. If our moon was much smaller, as is ‘normal’ in our solar system, there may have been no era in which the Moon had a same anger size as the Sun (31 arcmin).
In more than 500 million years, the Moon’s orbit will be so much extended, that even in the best of circumstances (perigee) the eclipse will be annular (not cover the whole disk of the Sun).
When the Moon had just formed, it may have been 15 times closer! That’s a huge disk to move in front of the Sun, but there was nobody to witness it for a long time.

I'd say coincidence. But hey, maybe if it was possible to look at all technological civilizations that ever existed in the Universe, we'd find that they all have to have a satellite that closely matches their parent star in size to allow for fancy eclipses. Throw that in your Drake Equation and see how rare technological civilizations are.

Quite a few discussions here at the Asterisk devolve into definition games, as each of us has a sense of how we like to use certain words. That's how languages evolve, of course. In this case coincidence has two common meanings...

1. a remarkable concurrence of events or circumstances without apparent causal connection.
2. correspondence in nature or in time of occurrence.

I tend to use the word in its first meaning when talking about a scientifically explainable event like an eclipse. Our race's pre-scientific explanation for the near perfect match between the sizes of the Moon and the Sun certainly would have included the concept of coincidence, if only because we knew of no causal connection. But now we know better. However, as I said above, the fact we few are here now is a coincidence under the second meaning.

geckzilla wrote:I'd say coincidence. But hey, maybe if it was possible to look at all technological civilizations that ever existed in the Universe, we'd find that they all have to have a satellite that closely matches their parent star in size to allow for fancy eclipses. Throw that in your Drake Equation and see how rare technological civilizations are.

It may turn out that fairly large tides are vital in some way for the development of life, and therefore a large moon may be necessary. But I doubt that near total eclipses would be necessary to the devlopment of intelligence, as eclipses in general will be seen anyway -- occasionally, at least -- and will therefore prompt the curious mind to work out what they are.

geckzilla wrote:
I'd say coincidence. But hey, maybe if it was possible to look at all technological civilizations that ever existed in the Universe, we'd find that they all have to have a satellite that closely matches their parent star in size to allow for fancy eclipses. Throw that in your Drake Equation and see how rare technological civilizations are.

Surely it's a coincidence that they are nearly the same size at this time:

Sun: 31.6–32.7 arcminutes
Moon: 29.3 to 34.1 arcminutes

However, we know that the Moon's tidal force has proved us with a stable axial tilt for billions of years. And the Moon's tidal force has dominated the Sun's tidal force for those billions of years only because it's angular size has been as large or larger than that of the Sun .

Hence, it doesn't seem unreasonable to suggest that most of the technological civilizations that have ever existed in the Universe have had a satellite that either closely matches or exceeds their parent star in angular size (and thus allows for total eclipses).